The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 427–441 | Cite as

Universal non-equilibrium phenomena at submicrometric surfaces and interfaces

  • R. Cuerno
  • M. Castro
  • J. Munoz-García
  • R. Gago
  • L. Vázquez


The recent widespread interest in processes occurring at micro and nanometric scales has increased the physical relevance of the surfaces and interfaces constituting system boundaries, both at and far from equilibrium. In the latter case, universal properties occur, such as scale invariance (surface kinetic roughening), surface pattern formation or domain coarsening. However, descriptions of these systems feature limited predictive power when based merely on universality principles. We review examples from Materials Science at nano and submicrometric scales, that underlie the importance of describing growing surfaces by means of (phenomenological) constitutive laws, in order to correctly describe the rich behaviors experimentally found across many different systems. Additionally, this approach provides new generic models that are also of interest in the wider contexts of Pattern Formation and Non-Linear Science.


Pattern Formation European Physical Journal Special Topic Move Boundary Morphological Instability Vicinal Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. T.L. Hill, Thermodynamics of Small Systems (Dover, New York, 1994) Google Scholar
  2. A. Pimpinelli, J. Villain, Physics of Crystal Growth (Cambridge University Press, Cambridge, 1998) Google Scholar
  3. S.A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison-Wesley, Reading, 1994) Google Scholar
  4. J. García-Ojalvo, J.M. Sancho, Noise in Spatially Extended Systems (Springer-Verlag, New York, 1999) Google Scholar
  5. A.-L. Barabási, H.E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995) Google Scholar
  6. M.I. Rabinovich, A.B. Ezersky, P.D. Weidman, The Dynamics of Patterns (World Scientific, Singapore, 2000) Google Scholar
  7. M. Castro, R. Cuerno, R. Gago, L. Vázquez, Phys. Rev. Lett. 94, 016102 (2005) Google Scholar
  8. J. Muñoz-García, M. Castro, R. Cuerno, Phys. Rev. Lett. 96, 086101 (2006) Google Scholar
  9. T. Michely, J. Krug, Islands, Mounds, and Atoms (Springer, Heidelberg, 2004) Google Scholar
  10. Fluctuations and Scaling in Biology, edited by T. Vicsek (Oxford University Press, New York, 2001) Google Scholar
  11. A. Oron, S. Davis, S.G. Bankoff, Rev. Mod. Phys. 69, 931 (1997); T.M. Squires, S.R. Quake, ibid. 77, 977 (2005) Google Scholar
  12. R. Cuerno, L. Vázquez, in Advances in Condensed Matter and Statistical Physics, edited by E. Korutcheva, R. Cuerno (Nova Science, New York, 2004) Google Scholar
  13. D.D. Vvedensky, J. Phys.: Condens. Matter 16, R1537 (2004) Google Scholar
  14. J. Krug, in Collective Dynamics of Nonlinear and Disordered Systems, edited by G. Radons, P. Häussler, W. Just (Springer, Berlin, 2004) Google Scholar
  15. Frontiers in Surface and Interface Science, edited by C.B. Duke and E.W. Plummer (Elsevier, Amsterdam, 2002) Google Scholar
  16. P. Tabeling, Introduction to Microfluidics (Oxford University Press, New York, 2005) Google Scholar
  17. M.J. Madou, Fundamentals of Microfabrication (CRC Press, Boca Ratón, 2002) Google Scholar
  18. F. Ojeda, R. Cuerno, R. Salvarezza, L. Vázquez, Phys. Rev. Lett. 84, 3125 (2000); F. Ojeda, R. Cuerno, R. Salvarezza, F. Agulló-Rueda, L. Vázquez, Phys. Rev. B 67, 245416 (2003) Google Scholar
  19. P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995) Google Scholar
  20. P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977) Google Scholar
  21. G. Grinstein, Scale Invariance, Interfaces and Non-equilibrium Systems, edited by A. McKane, M. Droz, J. Vannimenus, D. Wolf (Plenum Press, New York, 1995) Google Scholar
  22. R. Cuerno, M. Castro, Physica A 314, 192 (2002) Google Scholar
  23. D.G. Cahill, J. Vac. Sci. Technol. A 21, S110 (2003) Google Scholar
  24. See a recent overview in U. Valbusa, C. Boragno, F. Buatier de Mongeot, J. Phys. Condens. Matter 14, 8153 (2002) Google Scholar
  25. S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, H.L. Hartnagel, Science 285, 1551 (1999); F. Frost, A. Schindler, F. Bigl, Phys. Rev. Lett. 85, 4116 (2000); R. Gago, L. Vázquez, R. Cuerno, M. Varela, C. Ballesteros, J.M. Albella, Appl. Phys. Lett. 78, 3316 (2001) Google Scholar
  26. D. Walgraef, Spatio-Temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science (Springer, New York, 1997) Google Scholar
  27. F. Frost, B. Ziberi, T. Höche, B. Rauschenbach, Nucl. Instrum. Methods Phys. Res. B 216, 9 (2004) Google Scholar
  28. M. Makeev, R. Cuerno, A.-L. Barabási, Nucl. Instrum. Methods Phys. Res. B 197, 185 (2002) Google Scholar
  29. A. Bray, Adv. Phys. 43, 357 (1994) Google Scholar
  30. W.H. Zurek, Phys. Rep. 276, 177 (1996); T.W.B. Kibble, in Patterns of Symmetry Breaking, edited by H. Arodz et al. (Kluwer Academic, New York, 2003) Google Scholar
  31. P. Tejedor, P. Šmilauer, C. Roberts, B.A. Joyce, Phys. Rev. B 59, 2341 (1999) Google Scholar
  32. P. Tejedor, M.L. Crespillo, B.A. Joyce, Appl. Phys. Lett. 88, 063101 (2006) Google Scholar
  33. J.W. Evans, P.A. Thiel, M.C. Bartelt, Surf. Sci. Rep. 61, 1 (2006) Google Scholar
  34. C. Schelling, G. Springholz, F. Schäffler, Thin Solid Films 369, 1 (2000) Google Scholar
  35. See contribution by M. Siegert to the volume in Grinstein95 Google Scholar
  36. A. Karma, Phys. Rev. E 48, 3441 (1993); O. Pierre-Louis, C. Misbah, Phys. Rev. B 58, 2259 (1998); 58, 2276 (1998) Google Scholar
  37. B. Davidovitch, E. Moro, H.A. Stone, Phys. Rev. Lett. 95, 244505 (2005) Google Scholar
  38. H. Emmerich, The Diffuse Interface Approach in Materials Science (Springer, Berlin, 2003) Google Scholar
  39. M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, New York, 1999) Google Scholar
  40. R. Cuerno, M. Castro, Phys. Rev. Lett. 87, 136103 (2001) Google Scholar
  41. C.H.J. Van den Brekel, A.K. Jansen, J. Cryst. Growth 43, 364 (1977); B.J. Palmer, R.G. Gordon, Thin Solid Films 158, 313 (1988); G.S. Bales, A.C. Redfield, A. Zangwill, Phys. Rev. Lett. 62, 776 (1989) Google Scholar
  42. H. Mori, Y. Kuramoto, Dissipative Structures and Chaos (Springer, Berlin, 1997) Google Scholar
  43. M. Castro, R. Cuerno, J.G. Buijnsters, L. Vázquez, preprint (2006); R. Cuerno, M. Castro, in Proceedings of the 4th. European Congress on Computational Methods in Applied Sciences and Engineering, edited by P. Neittaanmäki et al. (ECCOMAS, Jyväskylä, 2004) Google Scholar
  44. K. Sneppen, J. Krug, M.H. Jensen, C. Jayaprakash, T. Bohr, Phys. Rev. A 46, R7351 (1992) Google Scholar
  45. M. Nicoli, M. Castro, R. Cuerno (2006) (preprint) Google Scholar
  46. M. Castro, R. Cuerno, A. Sánchez, F. Domínguez-Adame, Phys. Rev. E 57, R2491 (1998); M. Castro, R. Cuerno, A. Sánchez, F. Domínguez-Adame, ibid. 62, 161 (2000) Google Scholar
  47. P. Schilardi, O. Azzaroni, R.C. Salvarezza, A.J. Arvia, Phys. Rev. B 59, 4638 (1999) Google Scholar
  48. H.-C. Kan, S. Shah, T. Tadyyon-Eslami, R.J. Phaneuf, Phys. Rev. Lett. 92, 146101 (2004) Google Scholar
  49. M.A. Auger, R. Gago, M. Fernández, O. Sánchez, J.M. Albella, Surf. Coat. Technol. 157, 26 (2002) Google Scholar
  50. M.A. Auger, L. Vázquez, O. Sánchez, M. Jergel, R. Cuerno, M. Castro, J. Appl. Phys. 97, 123528 (2005); M.A. Auger, L. Vázquez, R. Cuerno, M. Castro, M. Jergel, O. Sánchez, Phys. Rev. B 73, 045436 (2006) Google Scholar
  51. J.M. López, M.A. Rodríguez, R. Cuerno, Phys. Rev. E 56, 3993 (1997); J.J. Ramasco, J.M. López, M.A. Rodríguez, Phys. Rev. Lett. 84, 2199 (2000) Google Scholar
  52. P. Sigmund, Phys. Rev. 184, 383 (1969); J. Mat. Sci. 8, 1545 (1973) Google Scholar
  53. R.M. Bradley, J.M.E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988); R. Cuerno, A.-L. Barabási, Phys. Rev. Lett. 74, 4746 (1995) Google Scholar
  54. M. Castro, R. Cuerno, Phys. Rev. Lett. 94, 139601 (2005) Google Scholar
  55. O. Terzidis, P. Claudin, J.-P. Bouchaud, Eur. Phys. J. B 5, 245 (1998); A. Valance, F. Rioual, Eur. Phys. J. B 10, 543 (1999); Z. Csahók, C. Misbah, F. Rioual, A. Valance, Eur. Phys. J. E 3, 71 (2000) Google Scholar
  56. R. Gago, L. Vázquez, O. Plantevin, T. H. Metzger, J. Muñoz-García, R. Cuerno, M. Castro, Appl. Phys. Lett. 89, 233101 (2006) Google Scholar
  57. D. Flamm, F. Frost, D. Hirsch, Appl. Surf. Sci. 179, 95 (2001) Google Scholar
  58. T. Frisch, A. Verga, Phys. Rev. Lett. 96, 166104 (2006) cond-mat/0607553 (preprint) Google Scholar
  59. G.S. Bales, A. Zangwill, Phys. Rev. B 41, 5500 (1990) Google Scholar
  60. M. Raible, S.J. Linz, P. Hänggi, Phys. Rev. E 62, 1691 (2000) Google Scholar
  61. J. Muñoz-García, R. Cuerno, M. Castro, Phys. Rev. E 74, 050103(R) (2006) Google Scholar
  62. M. Raible, S.G. Mayr, S.J. Linz, M. Mokse, P Hänggi, K. Samwer, Europhys. Lett. 50, 61 (2000); M. Raible, S.J. Linz, P. Hänggi, Phys. Rev. E 64, 031506 (2001) Google Scholar
  63. J. Krug, Adv. Compl. Sys. 4, 353 (2001) Google Scholar
  64. P. Politi, C. Misbah, Phys. Rev. Lett. 92 (2004) 090601; Phys. Rev. E 73, 036133 (2006) Google Scholar
  65. A.A. Golovin, A.A. Nepomnyashchy, S.H. Davis, M.A. Zaks, Phys. Rev. Lett. 86, 1550 (2001) Google Scholar
  66. O. Pierre-Louis, C. Misbah, Y. Saito, J. Krug, P. Politi, Phys. Rev. Lett. 80, 4221 (1998); J. Kallunki, J. Krug, Phys. Rev. E 62, 6229 (2000); F. Gillet, O. Pierre-Louis, C. Misbah, Eur. Phys. J. B 18, 519 (2000) Google Scholar
  67. G. Danker, O. Pierre-Louis, K. Kassner, C. Misbah, Phys. Rev. E 68, 020601 (2003); Phys. Rev. Lett. 93, 185504 (2004) Google Scholar
  68. M. Castro, J. Muñoz-García, R. Cuerno, M. García-Hernández, L. Vázquez, New J. Physics (2006) (submitted) Google Scholar
  69. A.A. Nepomnhyaschy, Physica D 86, 90 (1995) Google Scholar
  70. H.G.E. Hentschel, J. Phys. A: Math. Gen 27, 2269 (1994); J.M. López, M. Castro, R. Gallego, Phys. Rev. Lett. 94, 166103 (2005) Google Scholar
  71. O. Pierre-Louis, Europhys. Lett. 72, 894 (2005) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • R. Cuerno
    • 1
  • M. Castro
    • 2
  • J. Munoz-García
    • 2
  • R. Gago
    • 3
  • L. Vázquez
    • 4
  1. 1.Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC)Universidad Carlos III de MadridLeganésSpain
  2. 2.Escuela Técnica Superior de Ingeniería and GISC, Universidad Pontificia de ComillasMadridSpain
  3. 3.Centro de Micro-Análisis de Materiales, Universidad Autónoma de MadridMadridSpain
  4. 4.Instituto de Ciencia de Materiales de Madrid (CSIC)MadridSpain

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